Stability and dwell time analysis of switched time delay systems

Abstract

Bu tez kapsam³nda zaman gecikmeli anahtarlamal³ geribeslemeli kontrol sis-temlerinin kararl³l³k analizinden bahsedilmi»stir. Bilinen herhangi bir zamanda,her /aday` sistem i»cin bir kontrol birimi tasarland³¸g³ farz edilmi»s ve bir son-raki anahtarlama an³na kadar de¸gi»smez bir geribeslemeli sistem elde edilmi»stir.Zaman gecikmeli sistemlerin kararl³l³¸g³n³ test eden LMI tabanl³ bir testin ko-runumlulu¸gu incelenmi»stir. Bu test, durma zaman³ analizi i»cin kullan³lmaktad³r.Bu testin s³n³rlamalar³ elde edildikten sonra, durma zaman³n³ eniyile»stirmek i»cintestte ge»cen serbest b³rak³labilir parametrelerin kesin s³n³rlar³ bulunmu»stur. Buama»cla basit tek dereceli sistemler ve daha yÄuksek dereceli sistemler ayr³ ayr³dikkate al³nm³»st³r. Ayn³ zamanda, zaman gecikmeli LQR tabanl³ anahtarlamal³geribeslemeli sistemler dikkate al³narak a¸g³rl³kland³rma matrisleri Q ve R'nindurma zaman³ Äuzerindeki etkileri incelenmi»stir.Anahtar Kelimeler: Zaman Gecikmeli Anahtarlamal³ Sistemler, Durma Zaman³,Kararl³l³k Analizi, Korunumluluk Analizi

In this thesis we deal with stability analysis of switched feedback system withtime delays. We assume that, at any given time for each /candidate` systema controller is designed and a ¯xed feedback system is obtained until the nextswitching instant. We investigate the conservativeness of an LMI-based stabilitytest for the time delay systems. This test is used for the dwell time analysis.After obtaining the limitations of this test, we ¯nd the exact bounds of allowableparameters appearing in the LMI-based test, in order to optimize the dwell time.For this purpose we consider simple ¯rst order systems and higher order systemsseparately. We also consider the LQR-based switched feedback controllers withtime delays and investigate the e®ects of weighting matrices Q and R on thedwell time.Keywords: Switched Time-Delay Systems, Dwell Time, Stability Analysis, Con-servativeness Analysis